Large-time optimal observation domain for linear parabolic systems
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910319716073472 |
|---|---|
| author | Mazari-Fouquer, Idriss Privat, Yannick Trélat, Emmanuel |
| author_facet | Mazari-Fouquer, Idriss Privat, Yannick Trélat, Emmanuel |
| contents | Given a well-posed linear evolution system settled on a domain $Ω$ of $\mathbb{R}^d$, an observation subset $ω\subsetΩ$ and a time horizon $T$, the observability constant is defined as the largest possible nonnegative constant such that the observability inequality holds for the pair $(ω,T)$. In this article we investigate the large-time behavior of the observation domain that maximizes the observability constant over all possible measurable subsets of a given Lebesgue measure. We prove that it converges exponentially, as the time horizon goes to infinity, to a limit set that we characterize. The mathematical technique is new and relies on a quantitative version of the bathtub principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03980 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large-time optimal observation domain for linear parabolic systems Mazari-Fouquer, Idriss Privat, Yannick Trélat, Emmanuel Analysis of PDEs Optimization and Control Given a well-posed linear evolution system settled on a domain $Ω$ of $\mathbb{R}^d$, an observation subset $ω\subsetΩ$ and a time horizon $T$, the observability constant is defined as the largest possible nonnegative constant such that the observability inequality holds for the pair $(ω,T)$. In this article we investigate the large-time behavior of the observation domain that maximizes the observability constant over all possible measurable subsets of a given Lebesgue measure. We prove that it converges exponentially, as the time horizon goes to infinity, to a limit set that we characterize. The mathematical technique is new and relies on a quantitative version of the bathtub principle. |
| title | Large-time optimal observation domain for linear parabolic systems |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2402.03980 |